Cows are, in fact, left to wither into old age. Having produced milk and calves, their meat is not desirable. Also, specially selected bulls are also kept alive for breeding purposes, so only the steers (castrated cattle) are killed.

But yeah, they generally don't let cows die of old age (costs way too much), once a cow reaches a certain age (I think it was 6-8 years, not 100% sure) they're usually slaughtered for their meat, which is used for either ground meats or animal food.

If a cow is too old the risk of mad cow disease is considered too high, so those cows are disposed of without using their meat for consumption.